On the cohomology of Lie algebras associated with graphs
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913693561782272 |
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| author | Aldi, Marco Butler, Andrew Gardiner, Jordan Grandini, Daniele Lichtenwalner, Monica Pan, Kevin |
| author_facet | Aldi, Marco Butler, Andrew Gardiner, Jordan Grandini, Daniele Lichtenwalner, Monica Pan, Kevin |
| contents | We describe a canonical decomposition of the cohomology of the Dani-Mainkar metabelian Lie algebras associated with graphs. As applications, we obtain explicit formulas for the third cohomology of any Dani-Mainkar Lie algebra and for the cohomology in all degrees of Lie algebras associated with arbitrary star graphs. We also describe a procedure to reduce the calculation of the cohomology of solvable Lie algebras associated with graphs through the Grantcharov-Grantcharov-Iliev construction to the cohomology of Dani-Mainkar Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the cohomology of Lie algebras associated with graphs Aldi, Marco Butler, Andrew Gardiner, Jordan Grandini, Daniele Lichtenwalner, Monica Pan, Kevin Rings and Algebras Combinatorics K-Theory and Homology We describe a canonical decomposition of the cohomology of the Dani-Mainkar metabelian Lie algebras associated with graphs. As applications, we obtain explicit formulas for the third cohomology of any Dani-Mainkar Lie algebra and for the cohomology in all degrees of Lie algebras associated with arbitrary star graphs. We also describe a procedure to reduce the calculation of the cohomology of solvable Lie algebras associated with graphs through the Grantcharov-Grantcharov-Iliev construction to the cohomology of Dani-Mainkar Lie algebras. |
| title | On the cohomology of Lie algebras associated with graphs |
| topic | Rings and Algebras Combinatorics K-Theory and Homology |
| url | https://arxiv.org/abs/2402.14188 |